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Lord of the Seven Kingdoms (feminine equivalent being Lady Regnant of the Seven Kingdoms) is the second title held by the ruler of the Seven Kingdoms, along with King of the Andals, the Rhoynar, and the First Men and Protector of the Realm.
This is loosely comparable to how some real-life medieval monarchies continued to claim titles that they no longer possessed de facto. The kings of England styled themselves "King of France" long after the English had lost all their French territory and any prospect of reclaiming it, and "Lord of Ireland" when they had little practical control of the country. The oddity of the early Targaryen kings laying claim to Dorne is that, unlike English kings who lost territory in Ireland but still claimed it, the Targaryens never conquered Dorne, nor did they have any other real legal claim to it.
In the books
Every king of the Targaryen dynasty held the title "Lord of the Seven Kingdoms", dating back to Aegon the Conqueror himself, even though Aegon was never able to conquer Dorne. He thus only controlled six of the seven kingdoms plus the Riverlands, which historically has never been counted as one of the "seven". Dorne only joined the Targaryen realm through peaceful marriage-alliance fully two centuries after the War of Conquest (about one century before the War of the Five Kings).
When Aegon I began his conquest of Westeros, he unilaterally declared himself king and lord of all of the Seven Kingdoms, before proceeding to actually conquer kingdoms such as the Reach or the Westerlands. Aegon's armies were repulsed from Dorne due to guerrilla warfare - but he never stopped claiming the title. Subsequent Targaryen kings continued to use the title "Lord of the Seven Kingdoms" as a tacit declaration that they still laid claim to Dorne and intended to conquer it eventually. A century and a half later, King Daeron I even managed to briefly conquer Dorne, but the occupation was thrown off and it remained independent for another half century.